Analog-to-digital conversion is a very important aspect in the processing of analog measurement signals. An analog-to-digital converter (ADC) samples the analog signal with predefined resolutions in time (the sampling rate) and signal quantity, respectively. In the following, the term “resolution” designates the resolution in signal quantity or amplitude resolution, i.e. the number of discrete levels over the range of the analog signal quantity, except when explicitly specified otherwise in the text. The resolution r of an analog-to-digital converter corresponds to the number of levels available to approximate the analog signal. When the resolution of an ADC is indicated as a number B of bits, the relationship between B and the resolution r is B=log2(r) or r=2B. Each digital sample corresponds to a discrete “reconstruction value”, which is one among the r possible digital values to which of the analog signal is mapped by the quantizer of the ADC at the times corresponding to the samples. The higher the resolution r, the more accurately the digital signal reproduces the analog signal. However, as analog-to-digital converters with a higher resolution are more expensive, their use in low-cost applications is often not possible for economical reasons.
If the analog signal quantity only changes by a small amount, the variation may not be visible in the digital signal. This is due to the limited resolution of the analog-to-digital converter. The minimum change in the analog signal that is required to guarantee, irrespectively of the initial value of the analog signal, a change in the digital signal is called the “step size” or “quantization step size”. If the analog signal changes by one step size, the digital signal undergoes a change corresponding to the addition or subtraction of one least significant bit (LSB).
According to a known method, the resolution of the conversion from an analog signal into a digital signal can be improved by adding white noise (Gaussian noise) on the analog signal before sampling. By modulating the analog signal with white noise, the digital values, obtained through the sampling, spread. Groups of subsequent samples of equal length are formed and an average is calculated over each group. The sequence of averages corresponds to a digital representation of the analog signal with higher resolution in signal quantity but with lower resolution in time. The method thus emulates an analog-to-digital conversion with lower sampling rate but higher resolution (or quantization).
Another method is described in the publication “TMS320C24x Family” from Texas Instruments Europe (Literature number: SPRA461, June 1998). The method uses a triangular signal instead of white noise to modulate the analog signal. The peak-to-peak amplitude of the triangular signal is chosen equal to the step size of the ADC or an integer multiple thereof. The analog modulated signal is sampled with a rate k times higher than the frequency of the triangular signal, where k=2, 4, 8, . . . “k” is called the oversampling factor. For each period of the triangular signal, k reconstruction values are obtained from the ADC. Averaging over the k reconstruction values yields a more accurate approximation of the analog signal, if the original analog signal can be assumed substantially constant on the time scale of one period of the modulation. To further increase the resolution, the oversampling factor k (which is equal to the number of sampling points per period of the triangular signal) has to be increased. When using a low-cost and, hence, slow, ADC, this will necessitate generating a triangular signal with a long period. However, to generate such a triangular wave with a large period, large capacitors and large resistors are required, which may not be available at low cost nor be convenient for demanding operation environments (for instance, some automotive manufacturers prohibit the use of resistors above 100 kΩ.) Furthermore, the electrical circuit as described in the publication “TMS320C24x Family” needs an additional amplifier to sum the analog signal and the triangular wave signal. Hence, it is desirable to find more cost efficient solutions.